Using a first-principles approach, we calculate Si 2p core-level shifts for spherosiloxane H8Si8O12 clusters chemisorbed on Si(001). A chemisorption mechanism that preserves the cage structure of the clusters is assumed. The resulting relaxed surface structure yields shifts consistent with the position and width of the peak at high binding energy in the photoemission spectrum. The role of dielectric effects on core-hole relaxation is essential to achieve this agreement. The other experimentally observed peaks at lower binding energies could not be accounted for by the chemisorption model considered here, suggesting that the actual surface structure is more complex.